## Hanson Finned Fishing with ALS

Here Bob Hanson’s technique of identifying finned fish through almost locked grids, as reported in Sudoku Assistant – Solving Techniques, is explained and recommended as part of the Sysudoku x-panel analysis. Kraken analysis, neglected by Hanson, is demonstrated to produce additional results with Bob’s examples.

In the previous post, I noted that Almost Locked Sets, or ALS, can be enumerated with the algorithm that I call the Suset scratchpad algorithm, that also lives inside Bob Hanson’s Sudoku Assistant. Here we are going to review a section of Bob’s SA report on the use of ALS to find effective finned fish. Finned fish violate the “lock” of n candidate locations along n lines, by having exta location, while nevertheless causing removals.

Bob’s first example is a finned 8-wing on two columns of this panel. Perhaps you’d like to find one of your own before peeking below. In the suset scratchpad starting list I selected the columns by increasing size, resolving ties left to right:

5   8     1     2       4       6       7

16, 25, 146, 126, 237, 1467, 1235

Susets are combined by taking the set union of column numbers and location(row) numbers. Our generated list includes ALS:

15   25     156     258

146, 126, 1467, 1256

That’s far enough. We’ve got two possible X-wings and two swordfish. Bob’s example is generated by the 25(columns)/126(rows) suset. Marking columns c2 and c5, a finned X-wing jumps into the boat. Now we search out the victims.

The process is described in Casting for Regular Fish, posted 4/3/12. We mark the columns in a spare row(|) and mark the victim rows in a spare column(+), then mark potential victims(v) in the victim row and not in the wing columns. Bob’s victim 8r1c1 is the one in the fin box. My post Krakening a Finned Fish of 4/10/12 tells what to do with the other potential victims, and why. All victims go free except those that “see” the fin. That accounts for Bob’s victim, but for the others, the potential kraken victims, we use the full definition of “seeing”, including ER and forcing chains.

Every finned fish has potential kraken victims. I endorse Bob’s technique as a way to find finned fish, but why is it that he never mentions the possibility of kraken fish? Here is the finned 8-wing, along with the results of the kraken analysis. I’m doing it myself these days. Virginia is away at camp.

All of the potential kraken victims escape, by seeing all other 8-candidates in one of the fin’s (f) units. Thus when each potential victim is present, it makes the fin a legitimate competitor for an 8 location.

Let’s note that Bob doesn’t mention the fin box, and gives a different rationale for the removal. It’s that 8r1c1 would remove both 1 and 2 from the sets of the ALS, namely {126, 16}. From this, it appears that Sudoku Assistant analysis of finned fish is limited to the special case of fin box removals.

But tell us, Bob, what would happen if we picked one of the other grid ALS that we found? Oh, never mind. I want to do it right here, to demonstrate what a productive idea your ALS finned fish finder really is.

The 15/146 suset gives us a surprise. It’s another finned fish with a victim in the fin box. But it’s a different box and a different victim!

Maybe the c25 8-wing victim was enough to solve the puzzle, but this is getting fascinating. What about the two finned swordfish that our ALS suset list beckons us with?

Again, we learn something by asking. The 156/1467 induced finned swordfish finds the same ALS uncovered victim, this time as a kraken swordfish. This demonstrates that finned fish go beyond   fin box removals.

But the 258/1256 finned swordfish goes a little crazy, as my kraken analysis of the c25 8-wing victim 8r1c1 reports that it forces both 8-candidates from c5. Bob’s grid ALS example is valid but the removal is justified more directly as an Andrew Stuart unit forcing chain, with either candidate in c5 forcing it out.

Bob’s second example, a finned swordfish on columns, is derived by

3/79, 6/278, 9/279 => 369/2789 .

I’ll bet you are curious about the alternative,

3/79, 6/278, 9/279 => 39/279 .

Go for it. I’ll checkpoint in my next post.

I’m curious about the further examples of Sudoku Assistant analysis that Bob presents in his SA report, so I’m devoting the next post to a checkpoint of your complete suset finned/kraken fish analysis of these examples. Get busy, there’s a lot to discover.